0=4(x^2-x+2)-(x+10)(x+2)

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Solution for 0=4(x^2-x+2)-(x+10)(x+2) equation: 


Simplifying
0 = 4(x2 + -1x + 2) + -1(x + 10)(x + 2)

Reorder the terms:
0 = 4(2 + -1x + x2) + -1(x + 10)(x + 2)
0 = (2 * 4 + -1x * 4 + x2 * 4) + -1(x + 10)(x + 2)
0 = (8 + -4x + 4x2) + -1(x + 10)(x + 2)

Reorder the terms:
0 = 8 + -4x + 4x2 + -1(10 + x)(x + 2)

Reorder the terms:
0 = 8 + -4x + 4x2 + -1(10 + x)(2 + x)

Multiply (10 + x) * (2 + x)
0 = 8 + -4x + 4x2 + -1(10(2 + x) + x(2 + x))
0 = 8 + -4x + 4x2 + -1((2 * 10 + x * 10) + x(2 + x))
0 = 8 + -4x + 4x2 + -1((20 + 10x) + x(2 + x))
0 = 8 + -4x + 4x2 + -1(20 + 10x + (2 * x + x * x))
0 = 8 + -4x + 4x2 + -1(20 + 10x + (2x + x2))

Combine like terms: 10x + 2x = 12x
0 = 8 + -4x + 4x2 + -1(20 + 12x + x2)
0 = 8 + -4x + 4x2 + (20 * -1 + 12x * -1 + x2 * -1)
0 = 8 + -4x + 4x2 + (-20 + -12x + -1x2)

Reorder the terms:
0 = 8 + -20 + -4x + -12x + 4x2 + -1x2

Combine like terms: 8 + -20 = -12
0 = -12 + -4x + -12x + 4x2 + -1x2

Combine like terms: -4x + -12x = -16x
0 = -12 + -16x + 4x2 + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
0 = -12 + -16x + 3x2

Solving
0 = -12 + -16x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + 16x + -3x2 = -12 + -16x + 3x2 + 12 + 16x + -3x2

Reorder the terms:
12 + 16x + -3x2 = -12 + 12 + -16x + 16x + 3x2 + -3x2

Combine like terms: -12 + 12 = 0
12 + 16x + -3x2 = 0 + -16x + 16x + 3x2 + -3x2
12 + 16x + -3x2 = -16x + 16x + 3x2 + -3x2

Combine like terms: -16x + 16x = 0
12 + 16x + -3x2 = 0 + 3x2 + -3x2
12 + 16x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + 16x + -3x2 = 0

Factor a trinomial.
(6 + -1x)(2 + 3x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {6, -0.6666666667}

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